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X-Ray Diffraction

By Cade Grigsby

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What can X-ray diffraction tell us?

• Structure– Bonds

• Length• Type

– Arrangement• Geometry of crystal

• Picture– Electron density map

• Diffraction– Angle– Intensity

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From X-Rays to Structure

"X ray diffraction" by Thomas Splettstoesser (www.scistyle.com) - own work; the public domain image Myoglobindiffraction.png [1] was used; the other images were rendered with PyMol (www.pymol.org) based on PDB id 1MBO. Licensed under CC BY-SA 3.0 via

Wikimedia Commons - http://commons.wikimedia.org/wiki/File:X_ray_diffraction.png#/media/File:X_ray_diffraction.png

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X-Rays

• Short wavelength– 0.01 nm to 10 nm

• High frequency– 30 petahertz (3.0E16) to 30 exahertz (3.0E19)

• High energy– 100 eV to 100 keV– Excites core electrons– Ionizing radiation– Deep penetration

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Discovery of X-Rays

• Wilhelm Conrad Rӧntgan– Discovered in 1895– Nobel prize in physics

1901

• Cathode ray tube– Lit up fluorescent screen

• First X-ray image

http://www.auntminnie.com/index.aspx?sec=ser&sub=def&pag=dis&ItemID=99329

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X-Rays on EM Spectrum

http://blog.gwcollegedemocrats.com/picsvqzp/x-rays-waves-produced

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Production of X-Rays

• Tungsten filament emits electron beam at target metal– Cu or Mo

• Beam excites core electrons of target– 1s electrons ionized• X-rays emitted as higher level electrons fall

• Higher atomic number means higher energy X-rays

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Ejection of electron

http://radiologymasterclass.co.uk/tutorials/physics/x-ray_physics_production.html#top_second_img

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Other mechanism for x-rays

• High energy electron slowed as it approaches nucleus– Energy lost in ‘braking’

process released as x-ray photon

http://radiologymasterclass.co.uk/tutorials/physics/x-ray_physics_production.html#top_second_img

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X-Ray Tube

http://pubs.usgs.gov/of/2001/of01-041/htmldocs/xrpd.htm

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Diffraction of Light

• Light bends passing edge of object

• Effect of opening width on bending

• Interference creates dark and light spots– Constructive– Destructive

http://www.inkscapeforum.com/viewtopic.php?f=5&t=7222

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Effect of slit width

http://people.whitman.edu/~dunnivfm/FAASICPMS_Ebook/CH1/1_3_2.html

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Single-slit diffraction

http://cronodon.com/Atomic/Photon.html

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Double-slit experiment

• Light is diffracted• Slit width approximately

equal to wavelength• Diffraction pattern– Wave interference

• Constructive• Destructive

http://astarmathsandphysics.com/ib-physics-notes/waves-and-oscillations/ib-physics-notes-youngs-double-slit-experiment.html

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Diffraction Patterns

• Single-slit diffraction– Constructive

interference– Destructive interference

• Double-slit diffraction– Constructive

interference– Destructive interference

• What happens with multi-slit diffraction?

http://ffden-2.phys.uaf.edu/webproj/212_spring_2014/Khan_Howe/TheDoubleSlitExperiment_KhanHowe/Home.html

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Multi-slit diffraction

http://labman.phys.utk.edu/phys136/modules/m9/diff.htm

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The Problem with X-Rays

• Electromagnetic waves diffract• Early experiments could not diffract X-rays– Wavelength too small

• New method for diffracting x-rays

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The Solution

• Diffraction occurs when slit equals wavelength– X-ray wavelength equal to size of atom

• Use crystal lattice structure to diffract• Diffraction pattern obtained

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Evidence of Diffraction

• Max von Laue, Walter Friedrich, and Paul Knipping in 1912

• Pass X-rays through CuSO4 crystal and collect image on photographic plate– Known as X-Ray

Crystallography

http://www.chemistryviews.org/details/ezine/2064331/100th_Anniversary_of_the_Discovery_of_X-ray_Diffraction.html

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Bragg’s Law

• William Lawrence Bragg and William Henry Bragg

• 2dsin(Θ) = nλ• Nobel Prize in Physics

1915

http://www.chemistryviews.org/details/ezine/2064331/100th_Anniversary_of_the_Discovery_of_X-ray_Diffraction.html

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Single crystal X-Ray diffraction

http://serc.carleton.edu/research_education/geochemsheets/techniques/SXD.html

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Power Diffraction

http://chemwiki.ucdavis.edu/Analytical_Chemistry/Instrumental_Analysis/Diffraction/Powder_X-ray_Diffraction

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Powder Analysis

http://photojournal.jpl.nasa.gov/jpeg/PIA16217.jpg

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First X-Ray Diffraction Pattern

• Interference pattern– White dots show

constructive interference– Dark space destructive

interference

• Intensity of light– Amount of interference– Relates to amplitude and

phase of X-rays

http://blazelabs.com/f-xray.asp

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Mechanism of Diffraction

• X-rays interact with core electrons– Scatter photons

• Light diffracted at specific angles

http://en.wikipedia.org/wiki/Bragg's_law

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Why diffraction points at specific angles?

• Angle of diffraction decreases as distance of planes increases– Reciprocal relationship

• Diffraction point distance from center decreases as distance between planes increases

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Patterns in Patterns

https://webspace.yale.edu/chem125/125/xray/laserdiffraction.htm

• Patterns of in benzene• Diffraction spots

perpendicular to planes

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Greater Plane Distance

https://webspace.yale.edu/chem125/125/xray/laserdiffraction.htm

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Along Planes of Symmetry

https://webspace.yale.edu/chem125/125/xray/laserdiffraction.htm

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Other Scattering

https://webspace.yale.edu/chem125/125/xray/laserdiffraction.htm

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Explained with Waves

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Greater distance between planes

• Increase distance of planes– Light goes in phase again– 5.0 cm distance between

planes– 45o angle of diffraction

from the horizontal

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Smaller Distance between Planes

• Higher angle of diffraction– Planes 2.0 cm apart– Angle 60o

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Crystal Structure

https://webspace.yale.edu/chem125/125/xray/laserdiffraction.htm

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Other Compounds

• Rosalind Franklin– X-Ray cystallographer

• B-form DNA• Dark spots areas of

constructive interferance• Strong bands top and

bottom– Base stacking– Small distance between

planes, high angle

http://undsci.berkeley.edu/article/0_0_0/dna_checklist

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Reason for Pattern

http://doublehelix.me/about/http://undsci.berkeley.edu/article/0_0_0/dna_checklist

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Further Reasoning

http://undsci.berkeley.edu/article/0_0_0/dna_checklist http://doublehelix.me/about/

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Watson and Crick

• Shown diffraction pattern by colleague of Franklin, Maurice Wilkins

• Recognized pattern– Worked with helical proteins

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What does this tell us?

• Interactions with core electrons• Electron density– Location of atoms• Center of electron density

– Type of bonds• Specific angles of diffraction– Unique to specific crystals– Miller indices

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From X-Rays to Structure

"X ray diffraction" by Thomas Splettstoesser (www.scistyle.com) - own work; the public domain image Myoglobindiffraction.png [1] was used; the other images were rendered with PyMol (www.pymol.org) based on PDB id 1MBO. Licensed under CC BY-SA 3.0

via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:X_ray_diffraction.png#/media/File:X_ray_diffraction.png

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The Transition

• How do you get from a diffraction pattern to an electron density map?– Computer programs

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Detection of Angles of Diffraction

• Diffractometers equipped with X-ray counters– Angle relative to crystal– Intensity of X-rays– Modern instruments coupled with CCD detectors

• Each element has specific angles of diffraction

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Diffraction Spectra of Si

http://www.mrc.iastate.edu/research_programs/nanocrystalline.htm

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Diffraction of NaCl

https://universe-review.ca/F13-atom04.htm

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Zinc Oxide Nano particles

http://openi.nlm.nih.gov/detailedresult.php?img=3289443_ijn-7-845f2&req=4

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Miller Indices

• Describes planes in a crystal

• Assign origin point• H, K, and L– Written (hkl)– Each distance written as

its reciprocal

http://commons.wikimedia.org/wiki/File:Miller_Indices_Cubes.svg

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More Miller Indices

http://oregonstate.edu/instruct/engr321/Exams/ExamsF02/ENGR321F02MTTwo.html

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Determination of Lattice Structure

• ‘a’ is lattice constant of cubic crystal

• ‘h’, ‘k’, and ‘l’ are the Miller indices of Bragg plane

• Without computer– Trial and error

http://en.wikipedia.org/wiki/Bragg%27s_law

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Body Centered Cube (BCC)

• h+k+l must equal an odd number

• Fe and W crystals

http://ecee.colorado.edu/~bart/book/bravais.htm

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Iron Crystal

http://pwatlas.mt.umist.ac.uk/internetmicroscope/micrographs/diffraction/bcc.html

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Face Centered Cube (FCC)

• h, k, l must be all odd or all even values

• Cu, Al, NaCl crystals

http://ecee.colorado.edu/~bart/book/bravais.htm

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Diffraction of NaCl

https://universe-review.ca/F13-atom04.htm

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Diamond FCC

• Atoms quarter of diagonal length apart

• h+k+l = 4n– Values must be all even

or all odd

• Si crystals

http://ecee.colorado.edu/~bart/book/bravais.htm

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Diffraction Spectra of Si

http://www.mrc.iastate.edu/research_programs/nanocrystalline.htm

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Electron Density Map• Constructed from

diffraction pattern• Slice of the crystal• Can be used to

determine information on bonds– Length and type

http://www.mdpi.com/1422-0067/8/2/103/htm

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Modern Electron Density Mapping

http://www.spring8.or.jp/wkg/BL41XU/solution/lang-en/SOL-0000001166?set_language=en&cl=en

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Other uses

http://www.portlandpress.com/pp/books/online/tiepac/session6/ch2.htm

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Analysis of Electron Density Map

• Contour rings– One represents 1e/Å

• Electronegative atoms– More contour rings

• Determination of bonds– Shortest are double bonds– Intermediate bonds are

resonance– Longest bonds are single

bonds

• No hydrogens– Too few electrons

https://webspace.yale.edu/chem125/125/xray/diffract.html

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Measuring Bonds

• Interpretation by comparison

• Measure from center of contours– Aromatic C—C bonds 1.5

cm– Double C=O bond 1.5 cm– Double C=C bond 1.1 cm– Single C—C and C—O

bonds 1.9 cm

• Computers can also perform calculations

https://webspace.yale.edu/chem125/125/xray/diffract.html

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Conclusion• Structure

– Miller Indices and computer programs• Crystal geometry

– Electron density map• Diffraction pattern

– Arrangement based on plane distance– Diffraction angle

• Identification of atoms– Specific diffraction angle– Rough estimate with electron density

• Bonds– Length– Type

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Questions?